# Thread: Win a birthday gift for your favorite skater

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## Win a birthday gift for your favorite skater

A couple of months ago our cerebral poster emiC won a GS trivia game by answering a mathematics question from ancient Egypt. The prize was a CD sent to her favorite skater for her/his birthday. EmiC's favorite skater is Jenny Kirk, and in August Jenny will receive a three CD collection of violin concertos performed by Hilary Hahn. Don't be surprised to see Jenny skating to the Beethoven, Brahms or Mendelssohn concertos next season.:lol:

Our resident musicologist Eltamina suggested that this would be a fun off-season game, a trivia contest with the prize being a CD sent as a birthday present to the winner's favorite skater. Eltamina has volunteered to choose (and buy!) the prizes, with music that reflects the personality and skating style of the recipient. Since these are real prizes, the questions are hard. Most of the questions will be about music, but I will start out with one about mathematics. Be the first to count the rabbit ears and claim your prize:

Farmer Bean keeps a mixed population of ducks and rabbits. One morning he counted them, and came up with a total of 310 heads and 758 feet. How many ears were there?

Mathman

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## hope i got it right

Mathman,

By my calculation, Farmer Bean has 69 Rabbits and 241 Ducks. Seeing as the last time I checked, Ducks don't have ears, that would mean that when Farmer Bean looks at his 310 heads, he will see 138 ears!

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## Re: hope i got it right

Oh no, I hoped that one would stay up more than 30 minutes! Which skater do you want to honor, and when is his/her birthday?

I see that we will have to make these harder. Give me a few minutes to get the next one up.

MM

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## skatingcanuck

Who is your favorite skater, when is his/her birthday. I will send a classical muisic cd for his/her birthday. We can start a birthday thread for him or her at GS.

I am math challenged, I won't even begin to solve this problem. You mean ducks don't have EARS!!!:rollin:

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## Re: skatingcanuck

I am so pleased to have won. The decision of whom to honour is so difficult, so I left it up to my 7 year old! My daughter would like Jennifer Robinson to be the recipient, and I think that is a fantastic choice! Jennifer's Birthday is December 2.

Huge thanks to both Mathman and Eltimina.

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## Re: Win a birthday gift for your favorite skater

WOW trivia/ quadriva are fun.

Congratulations sk8tngcanuck

OK, MM and Scanuck, I am curious how did you solve this problem.

I can see 69 rabbits heads + 241 duck heads = 310

I can also calculate 69 X 4 + 241 X 2 = 758

How did you work it backwards though? :rollin:

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## Re: skatingcanuck

<blockquote><strong><em>Quote:</em></strong><hr>My daughter would like Jennifer Robinson [/quote]

LOL, I love Jennifer Robinson too, I had the pleasure of watching her in SA 01, and worlds 03.

I checked her official site

skatinginc.com/Skaters/Robinson/home/

but I can't find a mailing address? Do you know her business mailing address, or can I send the cd to her c/o Skate Canada?

I think in early - mid November, we can start a Happy Birthday thread here at GS for Jennifer, then I can print out the thread and send that with the cd to Jennifer.

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## Re: skatingcanuck

Eltamina, I am stumped. I am not sure of how to get an address for her. I suppose either Skate Canada, or perhaps sending it c/o the Mariposa Club in Barrie may be another option.

Canuck

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## Re: skatingcanuck

<blockquote><strong><em>Quote:</em></strong><hr>How did you work it backwards though?[/quote]

Actually, this is at about 5th grade math level
r is # of rabbits
d is # of ducks

d + r = 310 (because there are 310 heads)
2d + 4r = 758 (because there are 758 feet, and ducks have 2 each, and rabbits have 4 each).

d+r=310 ~~> d=310-r
Now, we substritute this is the second equations, and get:
2*(310-r) + 4r = 758
620-2r+4r=758
2r=138
r=69

*******************************************
Mathman, come on, you can come up with something more challenging! Let's have some fun with this!

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## Re: skatingcanuck

<blockquote><strong><em>Quote:</em></strong><hr>Actually, this is at about 5th grade math level[/quote]

5th grade, I am so glad you weren't in my class, and my 5th grade math teacher did not grade on a curve. :rollin:

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## Re: skatingcanuck

All I meant was that the actual <em>math</em> behind this is 5th grade. I have a friend who works with kids preparing them for international math compatitions. He <em>loves</em> to bring in a really tough problem, and say something like "well, the math in this is like 3d grade", meaning that it's only arithmetic. Then I see my three friends: one with a Masters in Physics, one with a PhD in Math, and one working on his PhD in artificial intelligence struggling to solve it for the next hour!

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## Re: skatingcanuck

<strong>Skatingcanuck, I have email Skate Canada and asked them, hopefully they will reply soon.</strong>

I am sure some 5th graders are able to set up simu equations, I am sure some people can do simu equations in first grade. My question is whether the 5th grader next door armed with the skill of +, -, X and / is able to solve this problem. I think so. If the 5th grader has the discipline of keeping track of the UNITS.

The goal is to solve the total number of rabbit ears. So the 5th grader has to solve the mysterious number of rabbit heads.
Total number of rabbit feet + total number of duck feet = 758
310 – the mysterious number = total number of duck heads
total number of duck feet = (310 – the mysterious number) duck head X 2 feet/head, or after canceling the unit = (310 – mysterious number) X 2
total number of rabbit feet = Mysterious number of rabbit head X 4 feet /rabbit head, or after canceling the unit = 4 X mysterious number

Now the 5th grader can put everything together

4 X mysterious number + (310 – mysterious number) X 2 = 758
4 X mysterious number + 620 – 2 X mysterious number = 758
2 X mysterious number = 758 – 620
2 X mysterious number = 138

So the mysterious number of rabbit is 138 /2 = 69

Total number of rabbit ears = 69 rabbit X 2 ears/ rabbit = 138 ears (after canceling the unit)

Ah…. Lessons learnt from 5th grade

<strong>1. don’t panic
2. keep track of the units (if the units work out nicely, there is a good chance that the problem is solved, if the units do not work out nicely, try again)</strong>

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## Re: skatingcanuck

IMHO that's a mighty precocious fifth grader you've got there. I bet the average student couldn't do that problem until the ninth grade. The idea of "let x = the mystery number," and then write down everything that we know about x in the form of a set of equations -- that sounds like algebra to me. Not to mention, then you have to know how to solve the equations!

x + y = 310
2x + 4y = 758

Multiply the first equation by 2 and subtract the result from the second equation. This eliminates the x and leaves

2y = 138

which is the answer to the question. (We want to know 2y, so we don't really have to find x and y.)

Factoid: The word "algebra" comes from the title of a famous treatise on mathematics by the Arabian mathematician Abu al’Khwarizmi. (His name survives in the English word "algorithm.") The book was called "Hisab al-jabr w’al-muqabala," and the "al-jabr" part gave us the word "algebra."

Very roughly speaking, "al-jabr" means solving an eqaution by "doing the opposite operation" to both sides, and "muqabala" means "simplify the answer by collecting like terms." So to solve the equation

x + 3 = 5

first we do "al-jabr" by subtracting 3 from both sides:

x = 5 - 3,

and then we do "muqubala' by actually performing the subtraction:

x = 2.

So now you know. :lol: :lol: :lol:

Mathman

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## Lessons learnt from 5th grade

To this day, I still remember the lessons that were drilled into my brain in 5th grade as mentioned in my previous message.

1. don’t panic
2. keep track of the units (if the units work out nicely, there is a good chance that the problem is solved, if the units do not work out nicely, try again)

In addition, I was told to
3. Look at the whole picture or the entire problem, do not get bogged down in the minute things.

An example that was given to me was something similar to this

{417 X 396 + [(720 + 390)/10 - (6 square + 5 cube) X 13] } X0

Oh well, take one look at the whole thing, and hand the answer zero to your teacher and get some junior mints

MM,

The 5th grader in my example does not have to set up simultaneous equations like

x + Y = 310
and 4x + 2Y = 758

S/he just has to keep track of the units and maybe s/he is doing algebra w/o substituting x = mystery number of rabbits. Of course I couldn't do that even in the 12 th grade, but I am sure you were crunching these faster than Freddy splashing in his bath when you were 10 y/o.

Seriously, even though I did not major in math, I think it is so important for students to keep track of the units, and not be afraid or panic when they are solving problems.

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